How can I control when a camera starts moving along a curve
Just set keyframe where it is still, further in the timeline just before the other keyframes start moving the camera :) 
Like, if you want it to be still in half a second, place a keyframe at frame 12, and then have the other frames placed afterwards. If it is in the middle of a move section, then you need to place a keyframe where you want the camera to be still, and then place the same keyframe at the frame of how long you want the still camera to last :)

If this didn't explain your issue, please tell me, and I will try to understand the issue :)